That’s cool. As soon as a budget gets thrown out the window, it’s hard to know when to stop giving advice. 
Don’t go for the 960. The bandwidth is too small. GTX970 or 290X will be perfect.
When it comes to GPUs, PhysX only works on an Nvidia GPU, not an AMD GPU. As the Unreal Engine is (quite properly) platform agnostic, it chooses to only handle PhysX on the CPU, not the GPU, so you will make no gain there, and neither will any people playing your game.
IPS screens are about £100 in the UK, so probably about $100 in the US. They are all pretty good, and cheap as chips (compared to the £510 I spent on mine back in 2008). Also, the extra RAM would be a better choice than the GTX980.
Good thinking. However, a GTX980 is really only for bigger resolutions, and you will see no real gains at 1920x1080, so I would save my money, for another time.